Power System Analysis - Lecture 1: Introduction

403001POWER SYSTEM ANALYSISDr Nguyen Van LiemDepartment of Power SystemFaculty of Electrical and Electronics EngineeringLecture 1Introduction Simple Power SystemEvery power system has four major componentsgeneration: source of power, ideally with a specified voltage and frequencyTransmission system: transmits power; ideally as a perfect conductordistribution system: distributes power; ideally as a perfect conductorload: consumes power; ideally with a constant resistive valueComplicationsNo ideal voltage sources existLoads are seldom constantTransmission and distribution systems have resistance, inductance, capacitance and flow limitationsSimple system has no redundancy so power system will not work if any component fails Notation - PowerPower: Instantaneous consumption of energyPower Units 	Watts = voltage x current for dc (W)	kW 	–	1 x 103 Watt	MW 	– 	1 x 106 Watt	GW	–	1 x 109 WattInstalled U.S. generation capacity is about 900 GW ( about 3 kW per person)Maximum load of Champaign/Urbana about 300 MWNotation - EnergyEnergy: Integration of power over time; energy is what people really want from a power systemEnergy Units	Joule	= 	1 Watt-second (J)	kWh	– 	Kilowatthour (3.6 x 106 J)	Btu	– 	1055 J; 1 MBtu=0.292 MWhPower System ExamplesElectric utility: can range from quite small, such as an island, to one covering half the continentthere are four major interconnected ac power systems in North American, each operating at 60 Hz ac; 50 Hz is used in some other countries. Airplanes and Spaceships: reduction in weight is primary consideration; frequency is 400 Hz.Ships and submarines Automobiles: dc with 12 volts standardBattery operated portable systemsReview of PhasorsGoal of phasor analysis is to simplify the analysis of constant frequency ac systems	v(t) = Vmax cos(wt + qv)	i(t) = Imax cos(wt + qI)Root Mean Square (RMS) voltage of sinusoidPhasor RepresentationPhasor Representation, cont’d(Note: Some texts use “boldface” type for complex numbers, or “bars on the top”)Advantages of Phasor Analysis (Note: Z is a complex number but not a phasor)RL Circuit ExampleComplex PowerComplex Power, cont’dComplex Power (Note: S is a complex number but not a phasor)Complex Power, cont’dConservation of PowerAt every node (bus) in the systemSum of real power into node must equal zeroSum of reactive power into node must equal zeroThis is a direct consequence of Kirchhoff’s current law, which states that the total current into each node must equal zero.Conservation of power follows since S = VI*Conversation of Power ExampleEarlier we foundI = 20-6.9 ampsPower Consumption in DevicesExampleFirst solvebasic circuitExample, cont’dNow add additionalreactive power loadand resolvePower System NotationPower system components are usually shown as“one-line diagrams.” Previous circuit redrawnArrows areused to show loadsGenerators are shown as circlesTransmission lines are shown as a single lineReactive CompensationKey idea of reactive compensation is to supply reactivepower locally. In the previous example this canbe done by adding a 16 MVAr capacitor at the loadCompensated circuit is identical to first example withjust real power loadReactive Compensation, cont’d Reactive compensation decreased the line current from 564 Amps to 400 Amps. This has advantages Lines losses, which are equal to I2 R decreaseLower current allows utility to use small wires, or alternatively, supply more load over the same wiresVoltage drop on the line is lessReactive compensation is used extensively by utilitiesCapacitors can be used to “correct” a load’s power factor to an arbitrary value. Power Factor Correction ExampleDistribution System CapacitorsBalanced 3 Phase () SystemsA balanced 3 phase () system hasthree voltage sources with equal magnitude, but with an angle shift of 120equal loads on each phaseequal impedance on the lines connecting the generators to the loads Bulk power systems are almost exclusively 3Single phase is used primarily only in low voltage, low power settings, such as residential and some commercialBalanced 3 -- No Neutral CurrentAdvantages of 3 PowerCan transmit more power for same amount of wire (twice as much as single phase)Torque produced by 3 machines is constantThree phase machines use less material for same power ratingThree phase machines start more easily than single phase machinesThree Phase - Wye ConnectionThere are two ways to connect 3 systemsWye (Y)Delta ()Wye Connection Line VoltagesVanVcnVbnVabVcaVbc-VbnLine to linevoltages arealso balanced (α = 0 in this case)Wye Connection, cont’dDefine voltage/current across/through device to be phase voltage/currentDefine voltage/current across/through lines to be line voltage/currentDelta ConnectionIcaIcIabIbcIaIbThree Phase Example	Assume a -connected load is supplied from a 3 13.8 kV (L-L) source with Z = 10020WThree Phase Example, cont’dDelta-Wye TransformationDelta-Wye Transformation ProofDelta-Wye Transformation, cont’dThree Phase Transmission Line